Essay Lab | Math Shack | Videos
TABLE OF CONTENTS
Use the <em>p</em>-test to determine if
converges or diverges.
Since the integrand is of the form where p > 1 and the interval of integration is [0,1], this integral diverges.
Piece of cake, right? The hard part is remembering when you want p > 1 and when you want p < 1.
There's a great trick for that: you can get by with remembering just one integral. The integral
converges because gets close to the x-axis quickly as x approaches ∞. If you can remember this, then you can remember that
because you have an example where p = 2 is greater than 1 and the integral converges. That means
We switch between p > 1 and p < 1 when we change the interval of integration from [1,∞) to [0,1], so this means
That's the whole p-test, and all we had to remember was that the integral
We recommend taking your time when using the p-test. It can be easy to get mixed up, even if you know what you're doing!